In a communications network such as the Optical Transport Network (OTN) defined in ITU-T Recommendation G.709 (G.709), which is hereby incorporated by reference herein, information is encoded in optical signals for transmission over optical fibers. Receivers are used to sample the optical signals for conversion into electrical signals for extraction and processing of the encoded information.
Light pulses traveling through fibers are subject to a number of adverse effects (often referred to as “impairments”), including chromatic dispersion (CD), polarization-mode dispersion (PMD) and polarization-dependent loss (PDL). CD is the phenomenon that light components of different wavelengths travel at different velocities, leading to the spreading of a pulse as it propagates along the fiber. The time spread due to CD is proportional to the dispersion parameter of the fiber, the bandwidth of the signal, the square of the light wavelength, and the length of the fiber. For high-speed long-haul optical links, the time spread can cover a few tens of to a few hundreds of the original pulse durations. As a result, hundreds of taps are required if a finite impulse response (FIR) filter is employed to compensate the effects of CD. To save computation, such a long FIR filter is often implemented in frequency domain by means of FFT/IFFT with overlap-and-add, as discussed for example in Rabiner, Lawrence R.; Gold, Bernard (1975) Theory and application of digital signal processing. Englewood Cliffs, N.J.: Prentice-Hall, which is hereby incorporated by reference herein. The dispersion parameter of a fiber varies slowly with environment such as temperature and moisture level.
PMD is caused by velocity difference between polarizations of traveling light. The resulting pulse spread, called differential group delay (DGD) is a few to a few tens of picoseconds for a typical fiber of length of a few thousand kilometers. For dual polarization (DP) signaling, PMD also causes multiplexing of the signals transmitted at two polarizations. Due to the random-walk nature of PMD effects, the multiplexing matrix is constantly rotating. The speed of the rotation can be up to several tens of thousands of radians per second. The fast time-varying nature of PMD requires a fast adaptive filter at the receiver. In a parallel implementation, which is often the case of high-speed communication systems, the block size must be kept small so that the multiplexing matrix is almost constant during a PMD filtering block. In addition to PMD, the signals of different polarizations may arrive at the receiver with different amplitude, leading to so-called PDL.
The demand of higher communication speed has spurred the recent research and development of DP coherent optical communication systems. In coherent reception of DP optical signals, the standard approach to channel equalization and polarization de-multiplexing employs two digital signal processing (DSP) components: a fixed equalizer and an adaptive equalizer comprising a multiple-input multiple-output (MIMO) filter. The fixed equalizer compensates the bulk of relatively static chromatic dispersion (CD) and is often implemented in frequency-domain for long-haul channels. The adaptive equalizer compensates polarization-mode dispersion (PMD), polarization-dependent loss (PDL), de-multiplexes the two polarization signals, and equalizes other channel impairments such as non-ideal filtering effects and any residual CD.
Examples of prior art equalization for coherent DP multiplexed optical signals are disclosed in the following publications, incorporated by reference herein in their entirety:                “Digital Filters for Coherent Optical receivers”, Optics Express, Vol. 16, Issue 2, pp. 804-817 (2008), by Seb J. Savory; (“Savory”); and        “Adaptive Crossing Frequency Domain Equalization (FDE) in Digital PolMux Coherent Systems”, US patent application publication, US 2010/0142952 A1, by Dayou Qian and Ting Wang. (“Qian”)        
FIG. 1 shows an example prior art two-stage hybrid frequency and time domain equalization system 100, similar to the system discussed by Savory. Such systems are currently widely used for real-time coherent optical systems. System 100 comprises a fixed frequency domain equalization (FDE) stage 110 followed by an adaptive time domain equalization stage comprising an adaptive multiple input multiple output (MIMO) filter 120. A pair of dual polarization signals H and V are received by overlapped fast Fourier transform (FFT) and inverse fast Fourier transform (IFFT) blocks 112 and 114, which compensate for CD as known in the art. The outputs of FFT/IFFT blocks 112 and 114 are resampled by resamplers 116 and 118, then passed to four MIMO filter branches 121-124 to compensate for PMD. The resampled signal from one polarization is passed to branches 121 and 122, and the resampled signal from the other polarization is passed to branches 123 and 124. The outputs of branches 121 and 123 are summed by adder 126, and the outputs of branches 122 and 124 are summed by adder 128, to produce output signals u(n) and v(n), respectively. With this structure, the latency of PMD compensator is only limited by the processing speed. Consequently, the timing information can be conveniently extracted at the output of PMD compensator (i.e. at the outputs of adders 126 and 128), and retiming is achieved by means of resamplers 116 and 118. The relatively small MIMO filter size also ensures negligible performance loss due to PMD rotation.
FIG. 2 shows an example prior art single stage adaptive frequency-domain equalization system 200, similar to the system disclosed by Qian. System 200 comprises FFT blocks 210 and 220 which receive dual polarization signals H and V, respectively. FFT block 210 transforms signal H into N frequency components, each of which components are passed to a pair of multipliers (schematically illustrated as multipliers 211-214 in FIG. 2, wherein the first frequency component is passed to multipliers 211 and 213 and the Nth frequency components is passed to multipliers 212 and 214). Likewise, FFT block 220 transforms signal V into N frequency components which are passed to multipliers 221-224. Each of multipliers 211-214 and 221-224 multiplies the received frequency component by a corresponding weighting coefficient (Wxx(1-N), Wxy(1-N), Wyx(1-N), Wyy(1-N)) received from FDE weight adaptation block 230. Each weighted frequency component is then summed with the corresponding weighted frequency component from the signal of the other polarization by adders 215, 216, 225, 226, before being transformed back to the time domain by IFFT blocks 217 and 227. The outputs of IFFT blocks 217 and 227 are then processed by overlap and add blocks 218 and 228, respectively.
System 200 resembles the first stage of the standard two-stage structure, i.e., the CD compensator. The difference is that the frequency-domain filter now has four sets of coefficients all of which need to be adapted. For large FFT size, these are a large number of filter taps to be adapted. This structure may lead to lower complexity but not suitable for optical links with large CD and fast PMD rotation, because the multiplexing matrix may change significantly during the processing of a large FFT/IFFT block. In addition, time tracking may not be able to take advantage of equalized data due to the large latency of the CD compensator.
The PMD MIMO filter is often by far the largest component in a digital coherent receiver for long-haul optical systems. Some PMD MIMO filters account for up to 50% or more of the total DSP gate counts in a typical ASIC design. The inventors have identified a need for improved methods and systems for reducing the complexity and power consumption required by PMD compensation in DP coherent optical transceivers.